The relation between time and distance is t=αx2+βx where α

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The relation between time and distance is

t = α x^{2} + β x

where

α

and

β

are constants. The retardation is

Options:

A . 2αv3

B . 2βv3

C . 2αβv3

D . 2β2v3

Answer: Option A
:
A

\frac{d t}{d x} = 2 α x + β

\Rightarrow v = \frac{1}{2 α x + β}

∵ a = \frac{d v}{d t} = \frac{d v}{d x} . \frac{d x}{d t}

a = v \frac{d v}{d x} = \frac{- v .2 α}{(2 α x + β)^{2}} = - 2 α . v . v^{2} = - 2 α v^{3}

∴

Retardation =

2 α v^{3}

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